2.2.3 Microgrid operator

P drive

and Pmax

for one time slot.

<sup>h</sup> is the equivalently consumed power of the h-th EV as if the EV route just lasts

<sup>h</sup> , <sup>t</sup> , <sup>T</sup> arr h

The state of charge (SOC) of EV battery at the starting point of a next time slot

Ph,EVð Þt Δt φh

<sup>h</sup> <sup>≤</sup> SOChð Þ<sup>t</sup> <sup>≤</sup> SOC max

When EVs are at home (from the arrival time to the next departure time), their

Ph,EVð Þt during EV plugged-in time is the decision variable and will be solved by the proposed algorithm. However, it is necessary to ensure that EVs have enough energy (SOC) for their routes before their departure times. To satisfy this requirement, we consider a simple EV charging strategy based on [21]–[22] in which Pmin

h,EV in (13) are specified during the EV plugged-in time. The EV charging

<sup>h</sup> to the next day <sup>T</sup>dep

h

The battery life function of EVs depends on EVs charging/discharging power

<sup>h</sup> , and the required state-of-charge SOCreq

EV ¼ const

EV ð Þ� <sup>t</sup> � <sup>t</sup><sup>0</sup> SOChð Þ� <sup>t</sup> SOCmin

� �=Δt � �

<sup>h</sup> )

h

h,EVðÞþt πhPh,EVð Þt Ph,EVð Þ t � 1 (18)

charging/discharging scheduling can be utilized for DR actions. The variable

SOChð Þþt φhPh,EVð Þt Δt : Ph,EVð Þt ≥0

� � ¼ �0:5<sup>P</sup> drive

: Ph,EVð Þt , 0

¼ 0 (14)

<sup>h</sup> (17)

<sup>h</sup> (15)

(16)

h,EV

� �

<sup>¼</sup> Ph,EV <sup>T</sup> arr h

depends on the SOC at the starting point of current time slot and a charging/

Ph,EV T dep

SOChð Þþt

SOC min

Ph,EV T dep h � �

> 8 ><

> >:

discharging efficiency φh, as shown in (4).

Research Trends and Challenges in Smart Grids

SOChð Þ¼ t þ 1

SOC constraint is as follows:

strategy is presented below.

1: Input: Departure time Tdep

2: <sup>t</sup><sup>0</sup> <sup>¼</sup> round Tdep

<sup>h</sup> ≤ t , t<sup>0</sup>

h,EVðÞ¼� <sup>t</sup> <sup>P</sup>min

h

h,EVðÞ¼ <sup>t</sup> max Pmin

h,EVðÞ¼ <sup>t</sup> min Pmax

3: If Tarr

4: Pmax

8: Pmin

9: Pmax

13: End

[23], as follows:

34

10: t ¼ t þ 1 11: Return to 3 12: Else <sup>t</sup> <sup>¼</sup> <sup>T</sup>dep h

5: t ¼ t þ 1 6: Return to 3 7: Else t<sup>0</sup> ≤ t , Tdep

Algorithm 1: EV charging strategy (from Tarr

h,EVðÞ¼ <sup>t</sup> <sup>P</sup>max

EV , Pmax

EV , SOCmax

Lhð Þ¼� Ph,EVð Þ<sup>t</sup> <sup>μ</sup><sup>h</sup> <sup>P</sup><sup>2</sup>

where μ<sup>h</sup> and π<sup>h</sup> are constant coefficients, h ¼ 1, …, v.

EV ¼ �Pmin

<sup>h</sup> � SOChð Þ<sup>t</sup> � �=Δ<sup>t</sup> � �

<sup>h</sup> � SOCreq h Pmax EV Δt � � The revenue function of the microgrid operator is calculated by

$$\mathcal{W}\_{\rm mg}\left(P\_{\rm g}(t), p(t)\right) = (p(t) - q(t))P\_{\rm g}(t) \tag{20}$$

where Pgð Þt is the power trading between the MG and the microgrid via the microgrid operator. In the case that the microgrid sells power to the MG, Pg ð Þt is negative. Furthermore, Pg ð Þt needs to satisfy upper and low bounds, as follows:

$$P\_{\mathcal{g}}^{\min} \le P\_{\mathcal{g}}(t) \le P\_{\mathcal{g}}^{\max} \tag{21}$$
